Consider a moral hazard example similar to the one we studied in class. The owners of...

  

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Consider a moral hazard example similar to the one we studied in class. The owners of a firm hire a manager to undertake a project. If the project is successful, it will earn profits for the owners of $420,000. If the project fails, it will earn $0 in profits. The manager will run the project and has discretion over whether or not she exerts (costly) effort to increase the likelihood of success. If manger exerts effort, the project succeeds with probability 0.5 and fails with probability 0.5. If manger does not exert effort, the project succeeds with probability 0.25 and fails with probability 0.75. The cost to the manager of exerting effort is $100,000. Assume here that the manager is risk neutral over how much income she earns (not risk averse as we assumed in class). In particular, her payoff from salary y is if no effort exerted y y - 100,000 if effort exerted Finally, suppose that the manager has an offer from another firm giving utility of 90,000 (you could think of this as a job offer with salary of $90,000 and no effort required). (a) What salary do the owners offer the manager if they do not want her to exert ef- fort? What is the owner's expected profit in this case? (You can take as given here that the owners pay the same salary regardless of whether the project succeeds or not.) (b) Suppose the owners want the manager to exert effort. Let ys denote the salary paid to the manager when the project is successful and yr denote the salary paid to the manager when the project fails. i. Write down the manager's participation constraint. ii. Write down the manager's incentive compatibility constraint. iii. Write down an expression for the owners' expected profits (i.e. as a function of ys and yF). iv. Argue that the manager's participation constraint will bind when the owners are choosing optimally. Use this to rewrite the owners' profit function and the manager's incentive compatibility constraint as a function of only yF. v. Show that the profit maximizing way to induce the manager to exert effort would has the owners paying the manager a negative salary if the project fails (i.e. the manager would have to pay the owners some amount if the project fails). What salaries ys and ye should the owners choose to maximize profit and incentivize the manager to exert effort? What is the owners' expected profit in this case? How might the owners implement the negative salary in reality? Consider a moral hazard example similar to the one we studied in class. The owners of a firm hire a manager to undertake a project. If the project is successful, it will earn profits for the owners of $420,000. If the project fails, it will earn $0 in profits. The manager will run the project and has discretion over whether or not she exerts (costly) effort to increase the likelihood of success. If manger exerts effort, the project succeeds with probability 0.5 and fails with probability 0.5. If manger does not exert effort, the project succeeds with probability 0.25 and fails with probability 0.75. The cost to the manager of exerting effort is $100,000. Assume here that the manager is risk neutral over how much income she earns (not risk averse as we assumed in class). In particular, her payoff from salary y is if no effort exerted y y - 100,000 if effort exerted Finally, suppose that the manager has an offer from another firm giving utility of 90,000 (you could think of this as a job offer with salary of $90,000 and no effort required). (a) What salary do the owners offer the manager if they do not want her to exert ef- fort? What is the owner's expected profit in this case? (You can take as given here that the owners pay the same salary regardless of whether the project succeeds or not.) (b) Suppose the owners want the manager to exert effort. Let ys denote the salary paid to the manager when the project is successful and yr denote the salary paid to the manager when the project fails. i. Write down the manager's participation constraint. ii. Write down the manager's incentive compatibility constraint. iii. Write down an expression for the owners' expected profits (i.e. as a function of ys and yF). iv. Argue that the manager's participation constraint will bind when the owners are choosing optimally. Use this to rewrite the owners' profit function and the manager's incentive compatibility constraint as a function of only yF. v. Show that the profit maximizing way to induce the manager to exert effort would has the owners paying the manager a negative salary if the project fails (i.e. the manager would have to pay the owners some amount if the project fails). What salaries ys and ye should the owners choose to maximize profit and incentivize the manager to exert effort? What is the owners' expected profit in this case? How might the owners implement the negative salary in reality?

Answer rating: 100% (QA)

a The owners offer the manager a salary of 210000 if they do not want her to exert effort The managers expected payoff from exerting effort is 0542000... View the full answer